Well, I'm going to offer a slightly different perspective. Yes I think breast feeding is a wonderful source for antibodies and immunity protection... However my personal view is that breast feeding (for calories, essential fats and proteins) is only as good as the mother own diet. And I'm sure that last sentence will tick off the pro-breastfeeding army. But I stand by it. I also have a different perspective because I do the non-milk diet for my daughter.
Cutting all dairy out of your diet will be difficult... Your pediatrician probably suggested giving up breast feeding because she realized how demanding of a dietary restriction it will be on you--plus she probably feels it is necessary to ensure there are no accidental milk traces in your daughter's diet. I am assuming that your daughter's hemoglobin levels will be retested in a few weeks?... So, the critical point will be whether her levels are more normal once her diet has been *absolutely* milk free beforehand. If you continue to breastfeed while you figure out your diet AND while your body cleans out milk protein traces, then that time period can't be seen as milk-free for your daughter... and the results for retesting will be tainted.
My daughter is allergic to cows milk. We did an entire year of the doctor, x-ray, blood test, antibiotic circus before I cut all forms of cow diary out of her diet (I tried to just cut out direct forms of dairy, but she still got sick. That's when I had to start reading labels...) Fortunately, she is only allergic to cows milk protein and can metabolize goat milk. However, your post uses the term "milk allergy" which could mean lactose intolerance (and that is not the same thing as a cows milk protein allergy). You ought to confirm with your pedi what exactly the allergy is... If she's allergic to lactose, then she can't metabolize and break down the sugar in milk (all milk); that is a lifelong allergy. If its an allergy to cows milk protein, your daughter may be able to digest goat milk--However some kids cannot have either goat milk or cows milk because goats and cows are closely related. Most kids outgrow a cows milk allergy between age 3-6 years.
I'm not a fan of soy protein (because of the way the body interprets it as the hormone estrogen) however if that is the only option for your daughter, then you go with soy. There is also a non milk, non-soy formula available.
If you decide to go for a non-milk diet for yourself, you will need to cut out all foods that contain "milk, casein, whey, butter". Start reading ingredient labels. Speaking from experience, its tough. Milk is in a lot of non-dairy things (like bread, crackers, margarine, salad dressing). And its hard to eat out... You're constantly asking what things are made with, were things cooked in butter. It is much easier to feed your small child a non-dairy diet than to maintain a non-dairy diet for yourself.
I will also mention that goat milk, goat yogurt, goat/sheep cheese is much more expensive than soy alternatives. So, one thing to consider is your home economics... What can you afford? We probably spend $250 per month on goat/sheep dairy products. I have become numb to the cost of groceries. I'm mentioning the cost factor because everyone will readily tell you not to go the soy route... However, there are other aspects to consider--mainly, the cost! No one seems to mention that as readily as all the negatives about soy.
I'm sure you will make the best decision for your baby. (And she will be fine!)